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what data structure for polinomial
10-07-2002
what data structure for polynomial
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math::polynomials(n) Tcl Math Library math::polynomials(n) __________________________________________________________________________________________________________________________________________________ NAME
math::polynomials - Polynomial functions SYNOPSIS
package require Tcl ?8.3? package require math::polynomials ?1.0.1? ::math::polynomials::polynomial coeffs ::math::polynomials::polynCmd coeffs ::math::polynomials::evalPolyn polynomial x ::math::polynomials::addPolyn polyn1 polyn2 ::math::polynomials::subPolyn polyn1 polyn2 ::math::polynomials::multPolyn polyn1 polyn2 ::math::polynomials::divPolyn polyn1 polyn2 ::math::polynomials::remainderPolyn polyn1 polyn2 ::math::polynomials::derivPolyn polyn ::math::polynomials::primitivePolyn polyn ::math::polynomials::degreePolyn polyn ::math::polynomials::coeffPolyn polyn index ::math::polynomials::allCoeffsPolyn polyn _________________________________________________________________ DESCRIPTION
This package deals with polynomial functions of one variable: o the basic arithmetic operations are extended to polynomials o computing the derivatives and primitives of these functions o evaluation through a general procedure or via specific procedures) PROCEDURES
The package defines the following public procedures: ::math::polynomials::polynomial coeffs Return an (encoded) list that defines the polynomial. A polynomial f(x) = a + b.x + c.x**2 + d.x**3 can be defined via: set f [::math::polynomials::polynomial [list $a $b $c $d] list coeffs Coefficients of the polynomial (in ascending order) ::math::polynomials::polynCmd coeffs Create a new procedure that evaluates the polynomial. The name of the polynomial is automatically generated. Useful if you need to evualuate the polynomial many times, as the procedure consists of a single [expr] command. list coeffs Coefficients of the polynomial (in ascending order) or the polynomial definition returned by the polynomial command. ::math::polynomials::evalPolyn polynomial x Evaluate the polynomial at x. list polynomial The polynomial's definition (as returned by the polynomial command). order) float x The coordinate at which to evaluate the polynomial ::math::polynomials::addPolyn polyn1 polyn2 Return a new polynomial which is the sum of the two others. list polyn1 The first polynomial operand list polyn2 The second polynomial operand ::math::polynomials::subPolyn polyn1 polyn2 Return a new polynomial which is the difference of the two others. list polyn1 The first polynomial operand list polyn2 The second polynomial operand ::math::polynomials::multPolyn polyn1 polyn2 Return a new polynomial which is the product of the two others. If one of the arguments is a scalar value, the other polynomial is simply scaled. list polyn1 The first polynomial operand or a scalar list polyn2 The second polynomial operand or a scalar ::math::polynomials::divPolyn polyn1 polyn2 Divide the first polynomial by the second polynomial and return the result. The remainder is dropped list polyn1 The first polynomial operand list polyn2 The second polynomial operand ::math::polynomials::remainderPolyn polyn1 polyn2 Divide the first polynomial by the second polynomial and return the remainder. list polyn1 The first polynomial operand list polyn2 The second polynomial operand ::math::polynomials::derivPolyn polyn Differentiate the polynomial and return the result. list polyn The polynomial to be differentiated ::math::polynomials::primitivePolyn polyn Integrate the polynomial and return the result. The integration constant is set to zero. list polyn The polynomial to be integrated ::math::polynomials::degreePolyn polyn Return the degree of the polynomial. list polyn The polynomial to be examined ::math::polynomials::coeffPolyn polyn index Return the coefficient of the term of the index'th degree of the polynomial. list polyn The polynomial to be examined int index The degree of the term ::math::polynomials::allCoeffsPolyn polyn Return the coefficients of the polynomial (in ascending order). list polyn The polynomial in question REMARKS ON THE IMPLEMENTATION
The implementation for evaluating the polynomials at some point uses Horn's rule, which guarantees numerical stability and a minimum of arithmetic operations. To recognise that a polynomial definition is indeed a correct definition, it consists of a list of two elements: the keyword "POLYNOMIAL" and the list of coefficients in descending order. The latter makes it easier to implement Horner's rule. BUGS, IDEAS, FEEDBACK This document, and the package it describes, will undoubtedly contain bugs and other problems. Please report such in the category math :: polynomials of the Tcllib SF Trackers [http://sourceforge.net/tracker/?group_id=12883]. Please also report any ideas for enhancements you may have for either package and/or documentation. KEYWORDS
math, polynomial functions CATEGORY
Mathematics COPYRIGHT
Copyright (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net> math 1.0.1 math::polynomials(n)